Feynman on the Scientific Method

Feynman on the Scientific Method

O.K., that is the present situation. 

Now I am going to discuss how we would look for a new law. In general we look for a new law by the following process. First we guess it. Then we compute the consequences of the guess to see what would be implied if this law that we guessed is right. Then we compare the result of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works. If it disagrees with experiment it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is — if it disagrees with experiment it is wrong. That is all there is to it. 

It is true that one has to check a little to make sure that it is wrong, because whoever did the experiment may have reported incorrectly, or there may have been some feature in the experiment that was not noticed, some dirt or something; or the man who computed the consequences, even though it may have been the one who made the guesses, could have made some mistake in the analysis. These are obvious remarks, so when I say if it disagrees with experiment it is wrong, I mean after the experiment has been checked, the calculations have been checked, and the thing has been rubbed back and forth a few times to make sure that the consequences are logical consequences from the guess, and that in fact it disagrees with a very carefully checked experiment. 

This will give you a somewhat wrong impression of science. It suggests that we keep on guessing possibilities and comparing them with experiment, and this is to put experiment into a rather weak position. In fact experimenters have a certain individual character. They like to do experiments even if nobody has guessed yet, and they very often do their experiments in a region in which people know the theorist has not made any guesses. For instance, we may know a great many laws, but do not know whether they really work at high energy, because it is just a good guess that they work at high energy. Experimenters have tried experiments at higher energy, and in fact every once in a while experiment produces trouble; that is, it produces a discovery that one of the things we thought right is wrong. In this way experiment can produce unexpected results, and that starts us guessing again. 

One instance of an unexpected result is the mu meson and its neutrino, which was not guessed by anybody at all before it was discovered, and even today nobody yet has any method of guessing by which this would be a natural result. 

You can see, of course, that with this method we can attempt to disprove any definite theory. If we have a definite theory, a real guess, from which we can conveniently compute consequences which can be compared with experiment, then in principle we can get rid of any theory. There is always the possibility of proving any definite theory wrong; but notice that we can never prove it right. Suppose that you invent a good guess, calculate the consequences, and discover every time that the consequences you have calculated agree with experiment. The theory is then right? No, it is simply not proved wrong. In the future you could compute a wider range of consequences, there could be a wider range of experiments, and you might then discover that the thing is wrong. 

That is why laws like Newton's laws for the motion of planets last such a long time. He guessed the law of gravitation, calculated all kinds of consequences for the system and so on, compared them with experiment — and it took several hundred years before the slight error of the motion of Mercury was observed. During all that time the theory had not been proved wrong, and could be taken temporarily to be right. But it could never be proved right, because tomorrow's experiment might succeed in proving wrong what you thought was right. We never are definitely right, we can only be sure we are wrong. 

However, it is rather remarkable how we can have some ideas which will last so long. One of the ways of stopping science would be only to do experiments in the region where you know the law. But experimenters search most diligently, and with the greatest effort, in exactly those places where it seems most likely that we can prove our theories wrong. In other words we are trying to prove ourselves wrong as quickly as possible, because only in that way can we find progress. 

For example, today among ordinary low energy phenomena we do not know where to look for trouble, we think everything is all right, and so there is no particular big program looking for trouble in nuclear reactions, or in super-conductivity. In these lectures I am concentrating on discovering fundamental laws. The whole range of physics, which is interesting, includes also an understanding at another level of these phenomena like super-conductivity and nuclear reactions, in terms of the fundamental laws. But I am talking now about discovering trouble, something wrong with the fundamental laws, and since among low energy phenomena nobody knows where to look, all the experiments today in this field of finding out a new law, are of high energy. 

Another thing I must point out is that you cannot prove a vague theory wrong. If the guess that you make is poorly expressed and rather vague, and the method that you use for figuring out the consequences is a little vague — you are not sure, and you say, 'I think everything's right because it's all due to moogles, and moogles do this and that more or less, and I can sort of explain how this works ... ', then you see that this theory is good, because it cannot be proved wrong! 

Also if the process of computing the consequences is indefinite, then with a little skill any experimental results can be made to look like the expected consequences. You are probably familiar with that in other fields. 'A' hates his mother. The reason is, of course, because she did not caress him or love him enough when he was a child. But if you investigate you find out that as a matter of fact she did love him very much, and everything was all right. Well then, it was because she was over-indulgent when he was a child! 

By having a vague theory it is possible to get either result. The cure for this one is the following. If it were possible to state exactly, ahead of time, how much love is not enough, and how much love is over-indulgent, then there would be a perfectly legitimate theory against which you could make tests. It is usually said when this is pointed out, 'When you are dealing with psychological matters things can't be defined so precisely'. Yes, but then you cannot claim to know anything about it. 

You will be horrified to hear that we have examples in physics of exactly the same kind. We have these approximate symmetries, which work something like this. You have an approximate symmetry, so you calculate a set of consequences supposing it to be perfect. When compared with experiment, it does not agree. Of course — the symmetry you are supposed to expect is approximate, so if the agreement is pretty good you say, 'Nice!', while if the agreement is very poor you say, 'Well, this particular thing must be especially sensitive to the failure of the symmetry'. 

Now you may laugh, but we have to make progress in that way. When a subject is first new, and these particles are new to us, this jockeying around, this 'feeling' way of guessing at the results, is the beginning of any science. 

The same thing is true of the symmetry proposition in physics as is true of psychology, so do not laugh too hard. It is necessary in the beginning to be very careful. It is easy to fall into the deep end by this kind of vague theory. It is hard to prove it wrong, and it takes a certain skill and experience not to walk off the plank in the game. 

In this process of guessing, computing consequences, and comparing with experiment, we can get stuck at various stages. We may get stuck in the guessing stage, when we have no ideas. Or we may get stuck in the computing stage. 

For example, Yukawa guessed an idea for the nuclear forces in 1934, but nobody could compute the consequences because the mathematics was too difficult, and so they could not compare his idea with experiment. The theories remained for a long time, until we discovered all these extra particles which were not contemplated by Yukawa, and therefore it is undoubtedly not as simple as the way Yukawa did it. 

Another place where you can get stuck is at the experimental end. For example, the quantum theory of gravitation is going very slowly, if at all, because all the experiments that you can do never involve quantum mechanics and gravitation at the same time. The gravity force is too weak compared with the electrical force. 

Because I am a theoretical physicist, and more delighted with this end of the problem, I want now to concentrate on how you make the guesses. As I said before, it is not of any importance where the guess comes from; it is only important that it should agree with experiment, and that it should be as definite as possible. 'Then', you say, 'that is very simple. You set up a machine, a great computing machine, which has a random wheel in it that makes a succession of guesses, and each time it guesses a hypothesis about how nature should work it computes immediately the consequences, and makes a comparison with a list of experimental results it has at the other end'. In other words, guessing is a dumb man's job. 

Actually it is quite the opposite, and I will try to explain why.  The first problem is how to start. You say, 'Well I'd start off with all the known principles'. But all the principles that are known are inconsistent with each other, so something has to be removed. 

We get a lot of letters from people insisting that we ought to makes holes in our guesses. You see, you make a hole, to make room for a new guess. Somebody says, 'You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn't just a lot of dots separated by little distances?' 

Or they say, 'You know those quantum mechanical amplitudes you told me about, they're so complicated and absurd, what makes you think those are right? Maybe they aren't right'. 

Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out. The problem is not only what might be wrong but what, precisely, might be substituted in place of it. 

In the case of the continuous space, suppose the precise proposition is that space really consists of a series of dots, and that the space between them does not mean anything, and that the dots are in a cubic array. Then we can prove immediately that this is wrong. It does not work. The problem is not just to say something might be wrong, but to replace it by something — and that is not so easy. As soon as any really definite idea is substituted it becomes almost immediately apparent that it does not work. 

The second difficulty is that there is an infinite number of possibilities of these simple types. It is something like this. You are sitting working very hard; you have worked for a long time trying to open a safe. Then some Joe comes along who knows nothing about what you are doing, except that you are trying to open the safe. He says 'Why don't you try the combination 10:20:30?' Because you are busy, you have tried a lot of things; maybe you have already tried 10:20:30. Maybe you know already that the middle number is 32 not 20. Maybe you know as a matter of fact that it is a five digit combination.... So please do not send me any letters trying to tell me how the thing is going to work. I read them — I always read them to make sure that I have not already thought of what is suggested — but it takes too long to answer them, because they are usually in the class 'try 10:20:30'.